Structured Prediction by Conditional Risk Minimization

Goh, Chong Yang; Jaillet, Patrick

doi:10.48550/arxiv.1611.07096

Cited by 1 publication

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“…Finally, we note that our framework is related to the general setting of structured prediction (see, e.g., Osokin et al (2017), Goh and Jaillet (2016) and the references therein). Motivated by problems in computer vision and natural language processing, structured prediction is a version of multiclass classification that is concerned with predicting structured objects, such as sequences or graphs, from feature data.…”

Section: Related Literaturementioning

confidence: 99%

Smart "Predict, then Optimize"

Elmachtoub¹,

Grigas²

2017

Preprint

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Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart "Predict, then Optimize" (SPO), which directly leverages the optimization problem structure, i.e., its objective and constraints, for designing better prediction models. A key component of our framework is the SPO loss function which measures the decision error induced by a prediction.Training a prediction model with respect to the SPO loss is computationally challenging, and thus we derive, using duality theory, a convex surrogate loss function which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions.Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest path and portfolio optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular when the prediction model being trained is misspecified.

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Section: Related Literaturementioning

confidence: 99%